Invariants
Level: | $104$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/104\Z)$-generators: | $\begin{bmatrix}55&72\\36&17\end{bmatrix}$, $\begin{bmatrix}75&56\\60&35\end{bmatrix}$, $\begin{bmatrix}87&74\\16&9\end{bmatrix}$, $\begin{bmatrix}95&30\\40&11\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.48.1.bi.2 for the level structure with $-I$) |
Cyclic 104-isogeny field degree: | $28$ |
Cyclic 104-torsion field degree: | $1344$ |
Full 104-torsion field degree: | $419328$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.48.0-8.e.1.3 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.48.0-104.h.2.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.48.0-104.h.2.20 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
104.48.1-104.d.1.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.48.1-104.d.1.17 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
104.192.1-104.g.2.1 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.w.1.5 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.bl.1.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.bp.2.4 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.bu.1.6 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.by.2.3 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.cf.2.6 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
104.192.1-104.ch.1.8 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.gm.1.8 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.gs.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ht.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.hz.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.mu.1.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.na.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.oa.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.og.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.288.9-312.sh.2.2 | $312$ | $3$ | $3$ | $9$ | $?$ | not computed |
312.384.9-312.jr.2.18 | $312$ | $4$ | $4$ | $9$ | $?$ | not computed |